2013 AMC 12A Problems/Problems 7

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x + (2/x) = y + (2/y)

((x^2)+2)/x = ((y^2)+2)/y

If we cross multiply,

y((x^2)+2) = x((y^2)+2)

(x^2)y + 2y = x(y^2) + 2x

(x^2)y - x(y^2) = 2x - 2y

xy(x-y) = 2(x-y)

xy = 2, which is D

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